• Corpus ID: 119261074

The directed landscape

@article{Dauvergne2018TheDL,
  title={The directed landscape},
  author={Duncan Dauvergne and Janosch Ortmann and B'alint Vir'ag},
  journal={arXiv: Probability},
  year={2018}
}
The conjectured limit of last passage percolation is a scale-invariant, independent, stationary increment process with respect to metric composition. We prove this for Brownian last passage percolation. We construct the Airy sheet and characterize it in terms of the Airy line ensemble. We also show that last passage geodesics converge to random functions with Holder-$2/3^-$ continuous paths. This work completes the construction of the central object in the Kardar-Parisi-Zhang universality class… 

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The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper to make it more accessible to probabilists.
A PATCHWORK QUILT SEWN FROM BROWNIAN FABRIC: REGULARITY OF POLYMER WEIGHT PROFILES IN BROWNIAN LAST PASSAGE PERCOLATION
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In last passage percolation models lying in the Kardar–Parisi–Zhang (KPZ) universality class, the energy of long energy-maximizing paths may be studied as a function of the paths’ pair of endpoint
Exponents governing the rarity of disjoint polymers in Brownian last passage percolation
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  • 2019
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In last passage percolation models lying in the KPZ universality class, the energy of long energy-maximizing paths may be studied as a function of the paths' pair of endpoint locations. Scaled
BULK PROPERTIES OF THE AIRY LINE ENSEMBLE BY DUNCAN DAUVERGNE
Abstract: The Airy line ensemble is a central object in random matrix theory and last passage percolation defined by a determinantal formula. The goal of this paper is to provide a set of tools which
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